Exercise 3.15 (Perturbation approach to lexicography) Consider a stan- dard form problem, under the usual assumption that the rows of A are linearly independent. Let e be a scalar and define E 2 b(e) = b + For every e > 0, we define the e-perturbed problem to be the linear programming problem obtained by replacing b with b(e). (a) Given a basis matrix B, show that the corresponding basic solution xb(e) in the e-perturbed problem is equal to B-'[b\I] m (b) Show that there exists some * > 0 such that all basic solutions to the E-perturbed problem are nondegenerate, for 0 0, we define the e-perturbed problem to be the linear programming problem obtained by replacing b with b(e). (a) Given a basis matrix B, show that the corresponding basic solution xb(e) in the e-perturbed problem is equal to B-'[b\I] m (b) Show that there exists some * > 0 such that all basic solutions to the E-perturbed problem are nondegenerate, for 0